The present invention relates to a method and apparatus for determining coefficients of friction. More particularly, the invention pertains to a microprocessor-based apparatus for receiving, and plotting on a visual display device, signals proportional to the acceleration of a block on a test surface, selecting a time point one or more times at which the coefficient of friction is to be computed, and displaying the computed coefficient.
Two bodies in contact experience mutual frictional forces. The force of kinetic friction operates when the body surfaces are moving relative to one another, while the force of static friction acts on bodies which are stationary with respect to each other. A block at rest on a surface may be placed in motion by applying a force to the block to overcome the static friction which keeps the block at rest. The maximum force of static friction will be the same as the smallest force necessary to start the block in motion. Once motion has started, this same amount of force produces an accelerated motion on the block since the frictional forces acting between the relatively moving surfaces usually are lower than static forces. A smaller applied force than that necessary to start a body in motion may keep the block in uniform motion without acceleration. This small applied force is equal in magnitude but opposite in direction to the force of kinetic or dynamic friction which is the resisting force between two relatively moving surfaces when that movement is occurring without interruption.
The coefficients of friction provide an indication of the degree of slipperiness between the two contacting surfaces. The coefficient of static friction is computed as the ratio of the magnitude of the maximum force of static friction to the magnitude of the normal force. The normal force is that force which a body exerts on the surface on which the body rests. For a block resting on a horizontal table or sliding along it, the normal force is equal in magnitude to the weight of the block. The coefficient of kinetic friction is computed as a ratio of the magnitude of the force of kinetic friction to the magnitude of the normal force. Generally, the coefficients of friction are values less than 1, and generally the static coefficient of friction exceeds the kinetic coefficient of friction.
There is a need in many circumstances to determine a surface's degree of slipperiness. Typically in the building construction industry, contractors are interested in knowing whether surfaces on which people are to walk are safe. Also, situations involving slip and fall accidents may require test analysis to determine whether the surface on which an individual fell could be considered dangerous. Manufacturers of floor polishes are also interested in safety testing surfaces coated with floor polishes being considered for marketing.
The results of slipperiness tests for surfaces are compared with established standards to determine if the surface is dangerous. The National Bureau of Standards established in 1948 a standard for the kinetic coefficient of friction. Research paper RP1879 reported that a slippery condition existed for a surface being tested if the coefficient of friction was less than 0.40.
The American Society of Testing and Materials established a standard that a static coefficient of friction of 0.50 or above is considered safe for a dry walkway surface. This standard is described in ASTM Standard D 2147-75. Various publications by the National Bureau of Standards recognize this 0.50 standard, and it is reported that the Underwriters Laboratories adopted this as an industry standard.
Generally, the static anti-slip coefficient of friction values have these meanings.
______________________________________ Coefficient Condition ______________________________________ .60 or above very safe .50 to .59 relatively safe .40 to .49 dangerous .35 to .39 very dangerous .00 to .34 unusually dangerous ______________________________________
A value below 0.50 means that the surface may be considered dangerous to walk on. The higher value indicating safety for static coefficients is valid since test results usually are higher for static than dynamic values obtained during tests of dry surface conditions.
Several known methods and apparatus have been used to determine the coefficients of friction of a surface. Some have provided information to determine the static coefficient, while others provided information to determine the kinetic coefficient. Since the concern primarily has involved the slipperiness of walkway and walking surfaces, these various devices have used a standard known surface to rest or slide on the surface to be tested. This standard surface has been a flat sanded smooth strip of shoe sole leather.
One such device to measure the coefficient of kinetic friction was developed during the 1940's and employed a pendulum. A strip of shoe leather was attached to the bottom of a weighted block rigidly suspended from a pivot point. A pointer extending from the pivot was attached to the pendulum. The block was raised arcuately to a predetermined height and released. The block swung along an arc towards and over the surface to be tested. After the block slid across the test surface, it continued its arcuate swing upward. The pointer moved upwardly with the block over an arcuately shaped gauge. The coefficient of kinetic friction could be computed using information from the gauge or from knowing the difference between the starting height and the height the block reached in its arcuate swing. This device, however, was not reliable because a portion of the energy was absorbed when the block struck the test surface at the bottom of the pendulum swing. Thus, the block having the shoe leather had to be carefully positioned over the test surface. Also friction created by the pendulum moving the pointer needle affected the results.
A second method used a machine having an articulated strut. A weight was pivotally connected to the upper end of a vertically disposed strut. The bottom of the strut was pivotally connected to a block which had a bottom lining of the test shoe leather. The leather rested on the surface to be tested. An increasing lateral force was applied to the block by rotating the strut until a slip of the block occurred. The coefficient of static friction could then be determined by finding the ratio of the lateral force to the known vertical force imposed by the weight at the upper end of the strut.
A third type of machine which measures the coefficient of friction involved dragging a block over the test surface. The block had a known weight and the bottom surface was lined with the test shoe leather. A force meter connected to the block measured the lateral pull necessary to begin movement of the block. That measurement permitted determination of the static coefficient of friction. Continued pulling of the spring kept the block in motion and sliding across the test surface. The amount of force necessary to keep the block in motion permitted determination of the coefficient of dynamic or kinetic friction.
These various devices, however, have limitations. One problem is that the different types of devices have yielded different results for the same surface. To properly evaluate the test results, one must be familiar with the type of equipment used and the effect on test results which arise from the various mechanical linkages involved in the apparatus.
Calibration of these testing machines is critical as well. Present test machines are generally difficult to calibrate against a national standard because of their inherent inaccuracies. Calibration involves using the machine on a surface, usually tile, having a known coefficient of friction.
Known types of friction meters also have had problems with accuracy and reproducibility of measurements and reliability of test results. For instance, in determining the coefficient of static friction, uncertainties arise when the stretching distances of the spring are measured. It is also time consuming to set up and carry out the number of tests necessary to provide confidence in the test results. It is likely that insufficient data is typically collected to obtain a suitable average for a friction coefficient. A large number of tests further may alter the characteristics of the surface being tested. Other errors are introduced when the kinetic coefficient of friction is measured. Traditional slip meters such as the drag type machine require pulling a block at a constant speed, since under ideal conditions the dynamic friction force equals the tension on the pulling string. The tension is measured with a spring balance. This approach leads to results that are reliable to only 10 or 15 percent, and are difficult to reproduce by other observers.
Faulconer U.S. Pat. No. 4,387,587 issued to describes an apparatus and processing methodology for acquiring the deceleration data of a motor vehicle which is skidding over a road surface to a stop. The device mounts to a car and in operation acquires data that may be used to determine the length of the skid and the kinetic coefficient of friction between the road surface and the skidding car.
The test apparatus described in the Faulconer reference includes an accelerometer which mounts to the car for sensing the deceleration of the car during a skid. (Since the car is slowing, the acceleration is negative and decreasing, and may be referred to as deceleration.) An analog signal proportional to the deceleration is generated at periodic intervals. This signal is converted to a digital value, i.e., digitized, and communicated to a microprocessor. The digitized value is stored together with an associated time value, and is subsequently used in computing the kinetic coefficient of friction, as well as computing other parameters related to the skidding of the car. Faulconer states that the values of acceleration and time may be recorded magnetically by a suitable recorder for computer processing at a later time, and that the data may be displayed on an x-y coordinate graphic mechanism.